{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XBBXZ3OR7YL2B4AM527ROJFAB5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4f9a12fa7bdb1f0f6f61e6a3d8b0b317aa6efff2b8344cb33eb501bbc00e0e4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-07-18T20:00:02Z","title_canon_sha256":"79f08aef16addf273da2364fbcd75e991d627144faece9f03612bf0cc3d79416"},"schema_version":"1.0","source":{"id":"1107.3557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3557","created_at":"2026-05-18T02:01:15Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3557v1","created_at":"2026-05-18T02:01:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3557","created_at":"2026-05-18T02:01:15Z"},{"alias_kind":"pith_short_12","alias_value":"XBBXZ3OR7YL2","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XBBXZ3OR7YL2B4AM","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XBBXZ3OR","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:1b47b4f7d5da499033e6934be19a7a3b442f690dc461e93c3ae207162ee899c4","target":"graph","created_at":"2026-05-18T02:01:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the Gibbons-Hawking metric for a three-dimensional periodic array of multi-Taub-NUT centers, containing not only centers with a positive NUT charge but also ones with a negative NUT charge. The latter are regarded as representing the asymptotic form of the Atiyah-Hitchin metric. The periodic arrays of Taub-NUT centers have close parallels with ionic crystals, where the Gibbons-Hawking potential plays the role of the Coulomb static potential of the ions, and are similarly classified according to their space groups. After a periodic identification and a Z2 projection, the array is tr","authors_text":"Harunobu Imazato, Masaya Yata, Shun'ya Mizoguchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-07-18T20:00:02Z","title":"Taub-NUT Crystal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3557","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:943a15954ebe9aabc4983653c5b790a7d9fdc7f17640e652b2dc94207daf4643","target":"record","created_at":"2026-05-18T02:01:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4f9a12fa7bdb1f0f6f61e6a3d8b0b317aa6efff2b8344cb33eb501bbc00e0e4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-07-18T20:00:02Z","title_canon_sha256":"79f08aef16addf273da2364fbcd75e991d627144faece9f03612bf0cc3d79416"},"schema_version":"1.0","source":{"id":"1107.3557","kind":"arxiv","version":1}},"canonical_sha256":"b8437cedd1fe17a0f00ceebf1724a00f57ab48a02dbb358169b2abf2e1523e05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8437cedd1fe17a0f00ceebf1724a00f57ab48a02dbb358169b2abf2e1523e05","first_computed_at":"2026-05-18T02:01:15.299666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:15.299666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/DjYskd3wTgabCJr3ta1Rm7G44XC9nlXjp/wugZFVALUnwNcrGrRPBDWHew5f+bBQZzrVWIRrj9EjHXCyLxeAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:15.300170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:943a15954ebe9aabc4983653c5b790a7d9fdc7f17640e652b2dc94207daf4643","sha256:1b47b4f7d5da499033e6934be19a7a3b442f690dc461e93c3ae207162ee899c4"],"state_sha256":"b5b0e94fe55935299771983d9fda33363b8daff27b99306bf1b72c1b1e3bc898"}